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Berger, M., Eisner, S., van der Ent, R., Flörke, M., Link, A., Poligkeit, J., Bach, V., Finkbeiner, M. (2018). Enhancing the Water Accounting and Vulnerability Evaluation Model: WAVE+. Environmental Science & Technology, 52(18), 10757–10766. https://doi.org/10.1021/acs.est.7b05164

Markus Berger, Stephanie Eisner, Ruud van der Ent, Martina Flörke, Andreas Link, Joseph Poligkeit, Vanessa Bach, Matthias Finkbeiner

Enhancing the Water Accounting and Vulnerability Evaluation Model: WAVE+

Accepted manuscript (Postprint)Journal article |

1

Enhancing the water accounting and vulnerability

evaluation model: WAVE+

Markus Berger1*, Stephanie Eisner2, Ruud van der Ent3, Martina Flörke4, Andreas Link1, Joseph

Poligkeit1, Vanessa Bach1, Matthias Finkbeiner1

1 Technische Universität Berlin, Chair of Sustainable Engineering, Straße des 17. Juni 135, 10623

Berlin, Germany

2 Norwegian Institute of Bioeconomy Research, P.O. Box 115, NO-1431 Ås, Norway

3 Utrecht University, Department of Physical Geography, Faculty of Geosciences, P.O. 80.115,

3508 TC Utrecht, The Netherlands

4 University of Kassel, Center for Environmental Systems Research, Wilhelmshöher Allee 47,

34109 Kassel, Germany

* Corresponding author: e-mail: markus.berger@tu-berlin.de; phone: +49.(0)30.314-25084

mailto:markus.berger@tu-berlin.de

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Abstract: Due to the increasing relevance of analyzing water consumption along product life

cycles, the water accounting and vulnerability evaluation model (WAVE) has been updated and

methodologically enhanced. Recent data from the atmospheric moisture tracking model WAM2-

layers is used to update the basin internal evaporation recycling (BIER) ratio, which denotes

atmospheric moisture recycling within drainage basins. Potential local impacts resulting from water

consumption are quantified by means of the water deprivation index (WDI). Based on the

hydrological model WaterGAP3, WDI is updated and methodologically refined to express a basin’s

vulnerability to freshwater deprivation resulting from the relative scarcity and absolute shortage of

water. Compared to the predecessor version, BIER and WDI are provided on an increased spatial

and temporal (monthly) resolution. Differences compared to annual averages are relevant in semi-

arid and arid basins characterized by a high seasonal variation of water consumption and

availability. In order to support applicability in water footprinting and life cycle assessment, BIER

and WDI are combined to an integrated WAVE+ factor, which is provided on different temporal

and spatial resolutions. The applicability of the WAVE+ method is proven in a case study on

sugarcane and results are compared to those obtained by other impact assessment methods.

Key words: water footprint, water consumption, life cycle assessment, life cycle impact

assessment, WAVE+

TOC Art:

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Introduction

In its recent report ‘Global Risks 2018’, the World Economic Forum rated the water crisis as one

of the main world’s challenges – even more severe than food and fiscal crises1. The awareness of

water scarcity related problems in many parts of the world and their link to daily products and

global trade has been raised by concepts like “Virtual Water2” or initiatives like the Water Footprint

Network3. More recently, methods assessing local impacts of water use along products’ life cycles

have been developed resulting in the establishment of an international water footprint standard

(ISO 14046)4.

Some of those impact assessment methods estimate the local consequences of water consumption

based on freshwater scarcity5-9. Other methods model the specific cause effect chain of water

consumption leading to potential damages on human health (due to malnutrition5, 10-11 or infectious

diseases10, 12), ecosystems (terestrial5, 13-14, aquatic15, coastal16, wetlands17), and freshwater

resources5, 18. Comprehensive reviews of existing approaches can be found in refs19-23.

One of the scarcity based impact assessment models is the water accounting and vulnerability

evaluation model (WAVE) published in Environmental Science and Technology four years ago8.

On the accounting level, the atmospheric evaporation recycling via precipitation within drainage

basins was considered for the first time, which can reduce water consumption volumes by up to

32%. In order to express local impacts of water consumption, WAVE analyzed the vulnerability of

basins to freshwater depletion based on local blue water scarcity. The water depletion index (WDI)

was determined by relating annual water consumption to availability (runoff) and additionally

considering water stocks (lakes and aquifers). In order to consider absolute freshwater shortage in

addition to relative scarcity and to avoid that dessert regions show a result of zero if consumption

is zero, WDI was set to the highest value in semi-arid and arid basins.

4

So far, the WAVE model provided factors for basin internal evaporation recycling and water

scarcity on a spatially explicit (basins and countries) but not on a temporally explicit level (monthly

data) used in recent methods9, 24. However, the three parameters water consumption, basin internal

evaporation recycling, and water scarcity are expected to show contrary effects during particular

seasons. For instance, in dry summer months water consumption can be higher than the annual

average, while the basin internal evaporation recycling could be lower and water scarcity can be

more severe than the annual means. These contrary effects are expected to lead to an accumulation

of inaccuracies when considering an annual temporal resolution. The lack of temporally explicit

factors is a severe shortcoming especially for agricultural goods which are produced during

particular seasons only.

In order to address the challenge of lacking temporal resolution in WAVE, to update the model

based on latest data and methodological findings, and to ease applicability, this work introduces

the WAVE+ model. WAVE+ provides a method for the accounting of water use and for assessing

potential local impacts of water consumption, which can be used in water footprinting according

to ISO 140464 and life cycle assessment according to ISO 1404425. The following sections present

the enhancements in the water accounting and the vulnerability evaluation models which can be

summarized as follows:

• Data update including increased temporal resolution (monthly) of the basin internal

evaporation recycling (BIER) ratio using the atmospheric moisture tracking model WAM2-

layers26

• Data update including increased temporal (monthly) and spatial (5 arcmin instead of 0.5

deg) resolution of the water depletion index (WDI) using WaterGAP327

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• Methodological refinements in the impact functionand increase in the discriminative power

of the WDI factors

• Integrated consideration of a basin’s vulnerability to freshwater deprivation resulting from

relative scarcity and absolute shortage of water

• Combination of BIER and WDI in an integrated WAVE+ factor promoting applicability

• Provision of WAVE+ factors for sub-basins and world regions in addition to basins and

countries

To enable a smooth reading and understanding, the updated results are presented and discussed

directly after the description of the methodological enhancements in each section. Subsequently, a

case study on the water footprint of sugarcane (to be precise: water scarcity footprint according to

ISO 14046) is presented to prove the applicability of the WAVE+ model and to compare results to

those obtained by other methods. Furthermore, methodological differences between the WAVE+

model, its predecessor version (WAVE)8, and the Available Water Remaining (AWARE)

consensus model9 of the Water Use in LCA (WULCA) group are discussed along with resulting

practical implications.

Water accounting model

Freshwater consumption denotes the fraction of water use (i.e. total withdrawal), which is not

returned to the originating basin due to evapo(transpi)ration, product integration, and discharge

into other watersheds or the sea28. In practice, water consumption in a basin n and month k (WCn,k)

is calculated by subtracting waste water discharges (WWn,k) from freshwater withdrawals (FWn,k).

However, this procedure neglects the fact that substantial shares of the evapo(transpi)rative water

consumption (En,k) and synthetically created vapor resulting from the combustion of fossil fuels

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(Vn,k) can be recycled within the atmosphere via precipitation in relatively short time and length

scales29-30.

Therefore, the WAVE+ model explicitly accounts for the shares of evapo(transpi)ration (ERn,k) and

synthetically created vapor (VRn,k) which are returned to the originating basin n in the month k via

precipitation as shown in Figure 1. Next to waste water discharges (WWn,k), those shares are

additionally subtracted from freshwater withdrawals (FWn,k) to determine the effective water

consumption (WCeff,n,k) (Equation 1).

WCeff,𝑛𝑛,𝑘𝑘 = FW𝑛𝑛,𝑘𝑘 − WW𝑛𝑛,𝑘𝑘 − ER𝑛𝑛,𝑘𝑘 − VR𝑛𝑛,𝑘𝑘 (1)

Figure 1. Basin (n) and monthly (k) specific water inventory flows along the life cycle of a

product considered in WAVE+

As shown in Equations 2a and 2b, the evaporation recycling (ERn,k) and vapor recycling (VRn,k)

within a basin n and month k are determined by multiplying volumes of evapo(transpi)ration (En,k)

and synthetically created vapor (Vn,k) with the basin internal evaporation recycling ratio (BIERn,k)

and the runoff fraction (αn,k).

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ER𝑛𝑛,𝑘𝑘 = 𝐸𝐸𝑛𝑛,𝑘𝑘 ∙ BIER𝑛𝑛,𝑘𝑘 ∙ 𝛼𝛼𝑛𝑛,𝑘𝑘 (2a)

VR𝑛𝑛,𝑘𝑘 = 𝑉𝑉𝑛𝑛,𝑘𝑘 ∙ BIER𝑛𝑛,𝑘𝑘 ∙ 𝛼𝛼𝑛𝑛,𝑘𝑘 (2b)

BIER represent the share of evapo(transpi)ration which is returned to the originating basin via

precipitation. It is calculated by means of local evaporation recycling length scales provided by the

updated atmospheric moisture tracking model WAM2-layers26 in a 1.5 deg resolution. Based on an

area-weighted average evaporation recycling length scale for each of the ca. 8.200 basins derived

from the hydrological model WaterGAP327, the BIER values presented in Figure 2 are determined

according to the procedure comprehensively described in the original WAVE method8. All maps

in this manuscript and in the supporting information were created using the ArcGIS software31.

8

Figure 2. Basin internal evaporation recycling (BIER) ratios denoting the fractions of evaporated

water returning to the originating basins via precipitation

As it can be seen in Figure 2, high BIER values above 30% can be found in South America, the

Himalayas and Central Africa. Thus, relevant shares of evapo(transpi)ration and synthetically

created vapor can be returned to the originating drainage basin via precipitation. However, these

regions show a strong seasonal variation. For example, the BIER values in the Congo basin range

from 0% in July to 50.2% in December. Since the share of evaporation recycling increases with

distance29, large drainage basins tend to show higher BIER values than small basins. Figure 2 also

9

shows that BIER is very low ( 60% in e.g. Ecuador and

Peru) or constantly low in some regions (< 20% in e.g. South Africa or Central Australia), it varies

strongly throughout the year in most of the world’s basins.

By multiplying BIERn,k (Figure 2) with αn,k (Figure S1), the runoff-relevant basin internal

evaporation recycling (BIERrunoff,n,k) is determined and shown in Figure S2 in the supporting

information. Since α is particularly low (< 40%) in Central Africa during those months in which

BIER is highest, large BIER ratios determined in e.g. the Congo basin (50.2% in December) are

reduced when considering the runoff fraction of the evaporation recycling (17.2% in December).

Even though BIERrunoff is below 5% in most of the world’s drainage basins and months, it reduces

blue water consumption significantly (10 - 28%) in basins in Central Africa, the Himalayas,

Ecuador and Peru during parts of the year.

In addition to the basin internal evaporation recycling (BIER), it would also be interesting to

consider the basin external evaporation recycling (BEER). As shown in Figure S3 in the

Supporting Information, BEER denotes the fraction of evapo(transpi)ration which returns as

precipitation to other than the originating basin. In this way it can be considered that

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evapo(transpi)ration which leaves the originating basin causes water consumption in the

originating basin but water gains in the receiving basins. However, predicting the exact locations

in which evaporation will return as precipitation is very complex and beyond the scope of this

work.

Vulnerability evaluation model

In addition to determining the effective water consumption on the volumetric level, WAVE+ aims

at analyzing the potential local impact that can result from water consumption in a particular basin

and month. Similar to other methods 5, 9, these impacts are defined as the risk to deprive other users

of using freshwater when consuming water. The risk of freshwater deprivation (RFD) can be

determined by multiplying the effective water consumption in each basin n and month k with its

corresponding water deprivation index (WDIn,k).

RFD = ���WCeff,𝑛𝑛,𝑘𝑘 ∙ WDI𝑛𝑛,𝑘𝑘�𝑘𝑘

(3)𝑛𝑛

WDIn,k denotes the vulnerability of a basin n to freshwater deprivation and, thus, expresses the

potential to deprive other users when consuming water in basin n and month k.

Most impact assessment indicators for water consumption5, 10, 32 are based on a ratio of annual water

consumption to availability and, thus, express relative freshwater scarcity only. Often this leads to

findings that very dry regions, like the Sahel zone or Central Australia, are not water scarce –

because consumption is close to zero33. In WAVE+ we assume that the vulnerability of a basin to

freshwater deprivation and thus, the impacts of water consumption, can be influenced by both

relative water scarcity and absolute water shortage. We therefore provide water deprivation indexes

for relative scarcity (WDIRS) and absolute shortage (WDIAS) and combine them into an integrated

index (WDI) as described in the following subsections.

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Water deprivation index based on relative water scarcity (WDIRS)

The development of WDIRS starts with a consumption-to-availability (CTA) ratio, which relates

annual water consumption (C) to availability (A). As comprehensively described in the original

WAVE method8, the CTA is enhanced to a more meaningful water scarcity indicator by

additionally considering surface water stocks (SWS) and an adjustment factor for the availability

of groundwater stocks (AFGWS). Recent data for consumption, availability (runoff), and surface

water stocks are derived from WaterGAP327. This model provides the data on a 5 arcmin resolution

which is aggregated to the basin level. Updated CTA* values, determined for each basin according

to Equation 4, are presented in Figure S4 in monthly resolution.

CTA𝑛𝑛,𝑘𝑘∗ =𝐶𝐶𝑛𝑛,𝑘𝑘

𝐴𝐴𝑛𝑛,𝑘𝑘 + SWS𝑛𝑛,𝑘𝑘∙ AFGWS,𝑛𝑛 (4)

The relevance of considering ground- and surface water stocks and the influence of parameter

settings in the underlying calculations has been analyzed by a set of sensitivity analyses in the

original WAVE paper. It reduces the result of the scarcity assessment by up to 20% in many water

abundant basins and, thus, increases the relative difference between water scarce and water

abundant regions. Since the calculation procedure and the underlying data have not changed

significantly, the main findings of these analyses are still considered valid.

By means of a logistic function (Figure 3) the physical scarcity ratio CTA* is translated into the

vulnerability of a basin to freshwater deprivation expressed by WDIRS, which can be understood

as an equivalent volume of water that another user has been deprived of due to a volume of water

consumed.

12

Figure 3. Logistic function determining WDIRS based on CTA*; S-curve leads to larger changes

in WDI resulting from changes in CTA* in medium scarcity ranges 0.125

13

should be noted that this setting represents a model choice to acknowledge that absolute water

shortage can influence the vulnerability of a basin to freshwater deprivation and, thus, the potential

to deprive other users when consuming water in this basin.

Figure 4. WDIAS determined as a function of the ratio of potential evapotranspiration (PET) to

precipitation (P)

Integrated water deprivation index (WDI)

After developing water deprivation indexes based on the relative scarcity and absolute shortage of

water as described above, an integrated WDI is determined as the maximum of WDIRS and WDIAS

(Figure 5). In most basins and months, WDIRS is decisive for the integrated WDI. Absolute water

shortage determines the integrated WDI in 28-39% of the basins.

14

Figure 5. WDI expressing the vulnerability of basins to freshwater deprivation

[m³deprived/m³consumed]

While WDI is constantly very low throughout the year (< 0.01) in large parts of Canada, South

America, Central Africa, and Russia, it is constantly very high (> 0.90) in most basins in Northern

Africa and the Arabian Peninsula. A strong seasonal variation can be observed in e.g. Argentina,

the north-eastern part of Brazil, India, Southern Europe, and the US.

15

In most of the world’s drainage basins WDI is either very low (blue) or very high (red) with only

few basins showing medium (green - orange) water stress. These rather binary results have already

been determined for the CTA* values expressing physical water scarcity (Figure S4 in the

supporting information). The effect has increased due to the logistic function, which translates

CTA* into WDI (Figure 3) This consideration of absolute water shortage in addition to relative

scarcity strongly influences the WDI results of particularly dry basins in Northern and Southern

Africa, the middle East, Central Asia, and Australia. The magnitude of this change is shown in

Figure S7 in the supporting information.

As any other impact assessment method for water use, WAVE+ assumes that impacts result from

a shortage of water and not from too much water, which can be relevant in basins and months with

high precipitation leading to risks of flooding, etc. Here water consumption could be considered

having a positive impact and evaporation recycling could be disadvantageously. However, this

impact pathway is beyond the scope of this work.

Combining water accounting and vulnerability evaluation: WAVE+ factors

The consideration of the basin internal evaporation recycling (BIER) and the evaluation of a basin’s

vulnerability to freshwater deprivation by means of WDI are considered as two separate steps

because BIER only applies to the evapo(transpi)rative fraction of consumptive water use. Other

forms of water consumption28, i.e. integration of water in products or discharge into other basins

and sea water, cannot be reduced by means of BIER. Moreover, it is intended to allow for a

consideration of the atmospheric recycling of synthetically created vapor, which requires to

determine the effective water consumption (Equation 1) before the analysis of local impacts

(Equation 3).

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However, in practice most water consumption occurs due to evapo(transpi)ration and the chemical

creation of water in the combustion of fossil fuels is rather low. Therefore, an integration of BIER

and WDI in the newly introduced WAVE+ factors is proposed, which is provided in addition to

the individual BIER and WDI factors. As shown in Equation 5, WAVE+n,k is determined by

reducing WDIn,k by the share of water returned to the originating basin n in month k as blue water

(BIERrunoff,n,k). WAVE+ factors are presented in Figure S8 in the supporting information. Since

BIER is relatively high in water abundant basins and relatively low in water scarce regions (Figure

S2 and S5), the difference between those basins is increased when combining BIER and WDI in

the WAVE+ factors.

WAVE+n,k = �1 − BIERrunoff,𝑛𝑛,𝑘𝑘� ∙ WDI𝑛𝑛,𝑘𝑘 (5)

The use of the integrated WAVE+ factors is recommended in cases in which evapo(transpi)ration

is the dominant form of water consumption (instead of product integration or discharge into other

basins or the sea) and in which no relevant amounts of synthetically created vapor are expected. In

such cases the risk of freshwater deprivation (RFD) can be determined by multiplying the basin

and month specific water consumption WCn,k with its corresponding WAVE+n,k factor and by

aggregating the results (Equation 6).

RFD = ���WC𝑛𝑛,𝑘𝑘 ∙ WAVE+𝑛𝑛,𝑘𝑘�𝑘𝑘

(6)𝑛𝑛

Spatial and temporal aggregation

The BIER, WDI and WAVE+ factors are determined on the level of drainage basins in a monthly

resolution. Even though this reflects hydrologic conditions best, inventory information on where

and when water consumption occurs along supply chains is often not available on such a detailed

geographic and temporal resolution. Therefore, the BIER, WDI and WAVE+ factors are

17

additionally provided in an aggregated form on the annual level and on the levels of countries and

world regions. The aggregation methodology and results are presented in the supporting

information.

Since the hydrological situation in humid and hyper-arid basins is rather constant throughout the

year, monthly WAVE+ factors presented in Figure S8 do hardly vary over the year and, thus, don’t

show significant differences to the annual average WAVE+ factors (Figure S9). Hence, a

temporally explicit assessment of water consumption in many basins in Russia or Northern Africa

is favorable but not urgently necessary. In contrast, a monthly assessment is highly relevant in

semi-arid and arid basins located in e.g. Chile, Spain or the US as severe changes throughout the

year have been identified in both atmospheric moisture recycling and water scarcity. Especially in

those regions a temporally explicit assessment of water consumption is strongly recommended for

agricultural product systems, which consume water during a particular season only.

Case study

In order to test the applicability of the WAVE+ model, to analyze the validity of results and to

compare the results to those obtained by other methods, a case study on the water footprint of sugar

cane production in Australia, Thailand and Columbia is conducted. Since only water consumption

but no pollution is considered, this study represents a water scarcity footprint according to ISO

14046.4

Based on the monthly and basin-specific blue water consumption of growing 1 t of sugarcane

provided by Pfister and Bayer24 and based on the production shares of the basins in a country, the

country-annual average blue water consumption of sugarcane has been determined. Depending on

the resolution of the impact assessment method, either the annual country average or the underlying

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monthly and basin-specific water consumption data can be used for analyzing the resulting local

consequences.

Subsequently, the water consumption is multiplied by the impact factors of the WAVE+ method,

the predecessor WAVE model8 as well as the AWARE9, WSI5, 24, and Eco-scarcity6 methods.

Results of the predecessor WAVE model8 have been determined by first reducing the water

consumption by the share of the basin internal evaporation recycling returning as blue water

(BIERrunoff) and then multiplying the effective water consumption with WDI. This procedure is

combined in the WAVE+ factors (Equation 5). Since WAVE+, AWARE and WSI provide monthly

and basin-specific impact factors in addition to an annual country average factor, they are applied

in both resolutions. Next to a comparison between countries, this allows for analyzing the

difference between an annual country average and a monthly and basin specific assessment.

Absolute results are shown in Table S1 in the supporting information.

Figure 6 shows the water consumption and impact assessment results of the WAVE, WAVE+,

AWARE, WSI and Eco-Scarcity methods on a relative scale normalized to the highest result of

each method. Differences in results obtained by the five methods are comprehensively discussed

in the supporting information.

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Figure 6. Relative presentation of blue water consumption for producing 1 t of sugar cane in

different countries and potential impacts determined by means of the WAVE, WAVE+,

AWARE, WSI, and Eco-scarcity methods (based on annual country average and monthly and

basin specific impact factors when possible)

Discussion

A specific discussion of the updated and methodologically enhanced BIER, α, BIERrunoff, WDI,

and WAVE+ factors as well as the interlinkages between them and the influence of methodological

choices has already been presented in combination with the results in the previous sections. A

general discussion on the consideration of BIER in water footprinting, the advanced water scarcity

assessment by means of WDI, and on further methodological aspects like the additional

consideration of water quality degradation has already been presented in the original WAVE

publication8. Since those findings are valid for WAVE+ as well, this section focuses on discussing

specific methodological aspects of the WAVE+ method and on the differences between WAVE+

and the predecessor WAVE model. Additionally, a discussion of methodological differences to the

AWARE model9 developed by the WULCA group is presented along with a quantitative

20

comparison of the impact factors. Additionally, practical implications of methodological

differences as well as hints when to use which method are provided.

Comparison WAVE+ and WAVE

The WAVE+ model presented in this work updates the data base of the predecessor version8 and

contains several methodological enhancements. The individual improvements of WAVE+

compared to WAVE are summarized in Table S2 in the supporting information and discussed

below.

Recent data from the atmospheric moisture tracking model WAM2-layers26 is used to update the

basin internal evaporation recycling (BIER) ratio. The main improvement of WAM2-layers is a

better representation of moisture tracking in a system with wind shear (e.g. in West Africa), by the

addition of a second atmospheric layer instead of merely having one layer. The horizontal moisture

transport with two layers (and vertical exchange between them) is more realistic than moisture

tracking with vertically integrated moisture fluxes. The main benefit is that moisture is not assumed

to instantly mix over the entire atmospheric column after evaporation. In the beginning it remains

in the lower atmosphere where winds are less strong. Hence, in most places the regional

evaporation recycling ratios in a grid increase. Thus, the length scales of the local evaporation

recycling decrease and BIER will increase in several basins (especially in temperate zones).

With regard to the vulnerability evaluation part of WAVE+, it should be noted that the term

“deprivation” used in RFD and WDI has replaced the term “depletion” used in the original WAVE

method. This has been done because the term water depletion is used in recent methodological

developments of the WULCA group modeling a concrete impact pathway to resource depletion35.

21

However, WDI is considered as a generic impact factor which does not consider a specific cause-

effect chain.

A relevant change compared to the predecessor WAVE model is the consideration of a basin’s

vulnerability to freshwater deprivation based on the relative scarcity and absolute shortage of water

by means of WDIRS and WDIAS, which are later combined to an integrated assessment (WDI).

For the determination of WDIRS latest hydrological data derived from the WaterGAP3 model27 is

used, which describes a climate period from 1981 to 2010 and increases the spatial resolution from

a 0.5 deg grid used in WaterGAP236-37 to a 5 arcmin resolution. Since the hydrological data is

aggregated from grid-scale to basins, the increased spatial resolution allows for a more precise

basin delineation and leads to a finer detailing of small coastal basins. This has increased the

number of basins from ca. 11,700 considered in WAVE to ca. 135,000 basins in WAVE+.

However, uncertainty can be high in very small basins (mainly consisting of one 5 arc minute grid

cell only) due to uncertainties in the coarse meteorological data driving WaterGAP3 and in the

physiographic input data. For this reasons basins < 1,000 km² have been merged with their nearest

valid neighbor basin (> 1,000 km²) within a distance of max. 100 km (Figure S11). If no basin >

1,000 km² was available within 100 km, small neighboring basins have been combined to basin

groups. In this way, WAVE+ distinguishes ca. 8,200 basins. Even though the absolute number of

basins decreased compared to WAVE, the basin delineation is more precise and the results are

more robust – especially for small coastal basins.

The monthly resolution of underlying hydrological data derived from WaterGAP3 allows for

refinements in the setting of the function translating physical scarcity (CTA*) into potential

impacts (WDIRS) : The logistic function shown in Figure 3 turns 1 at a CTA* of 0.5 (considered

as the threshold for severe water stress) instead of 0.25 in the predecessor WAVE model. Setting

22

WDIRS to 1 at a medium level of physical water stress was necessary because an annual average

CTA* of 0.25 implies that significantly higher water stress can occur during particular months38 –

especially in semi-arid regions. Fitting the S-curve to turn 1 at a CTA* of 0.5 in the new monthly

assessment is considered to reflect water stress more realistically and also led to a stronger

spreading of the WDIRS factors.

A main challenge in the determination of monthly WDIRS factors is the consideration of intra

annual storage capacities within basins24. This has partly been addressed due to the consideration

of reservoirs as well as ground- and surface water stocks in WDIRS. Moreover, a monthly temporal

resolution requires a higher spatial resolution in basins where the flow time from spring to mouth

is longer than one month24. Since a basin delineation has been used in which the 35 largest drainage

basins have been divided into sub-basins, the flow time is shorter than one month in each

(sub)basin.

Case studies39-40 conducted with the predecessor WAVE model have revealed a shortcoming

regarding the limited discriminative power of the WDIRS factors. Ranging from 0.01 to 1, impact

assessment results have been mainly influenced by the volume of water consumed. For example, a

water consumption of 1 liter in a highly water stressed region could not be identified as a hotspot

as long as a water consumption of more than 100 liters occurred in a water abundant region. For

this reason the spreading of WDIRS has been increased by one order of magnitude now ranging

from 0.001 to 1. As also discussed in the AWARE consensus model9, a spreading of the impact

factor by three orders of magnitude represents the best compromise to balance the influence of the

inventory and impact assessment phases on the water scarcity footprint result.

Concerning absolute water shortage, WAVE+ contains a separate indicator (WDIAS) which is

determined based on a ratio of potential evapotranspiration to precipitation (Figure 4). Compared

23

to setting WDI to the maximum in semi-arid and arid basin in a binary way in the predecessor

model, the new procedure enables a gradual analysis of potential impacts resulting from aridity.

By combining WDIAS and WDIRS to an integrated WDI, WAVE+ acknowledges that a basin’s

vulnerability to freshwater deprivation can be determined by the relative scarcity or absolute

shortage of freshwater.

When comparing BIER and WDI determined based on annual data of the predecessor WAVE

model to the annual BIER and WDI values of the WAVE+ model, which have been determined

based on consumption weighted averages of the underlying monthly data, several differences can

be observed. The annual average basin internal evaporation recycling tends to be lower in the

WAVE+ model. This can be explained by the fact that BIER is lower in dry months in which the

water consumption is usually higher. Due to the weighting based on monthly consumption shares,

the relatively low BIER values of those dry months dominate the annual averages. Comparing the

annual average WDI values of the WAVE+ model (Figure S10) to the WDI of the predecessor

version, a more diverse spreading of the WDI values can be observed. This is because the rather

binary WDI results obtained in WAVE+ on the monthly level have been obtained in a similar form

in WAVE on the annual level. However, in WAVE+ the seasonal variation between relatively low

water stress in the wet season and comparably high water stress in the dry season is balanced due

to the creation of annual averages.

In contrast to the predecessor version, the WAVE+ model provides integrated WAVE+ factors

which combine the consideration of BIER on the inventory level and the evaluation of potential

local consequences by means of WDI on the impact assessment level (Equation 5). In combination

with the provision of annual-, country-, and world region average WAVE+ factors in addition to

24

monthly, basin, and sub-basin specific factors, the applicability of the WAVE+ model has been

increased significantly.

Comparison WAVE+ and AWARE

A direct comparison between the WAVE+ and the WULCA group’s consensus model AWARE is

challenging since the two methods have partly different scopes and follow different modelling

approaches. AWARE does not consider effects of atmospheric evaporation recycling considered

by means of BIER in WAVE+. The impact assessment model is based on the available water

remaining after human and ecosystem water demands have been met (availability minus demand,

AMD). Instead of a difference, WAVE+ is based on a ratio of human consumption to availability

(considering ground and surface water stocks, CTA*) which is translated into a basins vulnerability

to freshwater depletion by means of a logistic function (WDIRS). .In order to acknowledge a basin’s

absolute water shortage, AMD is related to the basin’s area in the AWARE method. The inverse

of the basin’s area specific availability (low availability leads to high impacts) is divided by the

global average area specific availability. This ratio is used as the final impact factor in an interval

between 0.1 and 100 [m³world eq/m³]. In the WAVE+ method, absolute water shortage is considered

by a separate impact factor (WDIAS) which is determined based on a ratio of potential

evapotranspiration to precipitation. The integrated WDI varies by a factor of 1,000 as well (0.001

to 1) but is not put in relation to a global average because it expresses an equivalent volume of

water another user is deprived of due to a volume of water consumed [m³deprived/m³consumed].

A quantitative comparison of the annual and country average impact factors of WAVE+ and

AWARE is accomplished by means of a regression analysis presented in Figure S12 in the

supporting information. The comparison shows that the impact factors of most countries are higher

in WAVE+ than in AWARE on a relative level. The main reason for this is the different and more

25

stringent way of considering absolute water shortage in WAVE+ described above. As shown in

Figure S7, this setting significantly increases the WDI of many basins (and thus countries)

throughout the year. The correlation analysis also shows a few extreme outliers (Uganda, Rwanda

and Burundi) in which the relative AWARE factors are up to 200 times higher than the relative

WAVE+ factors. The reason for this can be found in the different water scarcity results in the

Kagera basin, which is the main basin of those three countries. As shown in Figure S13 in the

supporting information, this basin is considered as highly water scarce throughout the year in

AWARE and as water abundant throughout the year in WAVE+. The reason for this significant

difference is the consideration of the environmental water requirement (EWR) in the AWARE

method9, which is determined as a percentage (30-60%) of the pristine (without human

intervention) water availability. In case of the Kagera basin this percentage of the pristine

availability is even larger than the today’s water availability because surface runoff and

groundwater recharge have been strongly influenced by the extensive agricultural practice in this

region around Lake Victoria. For this reason, the available water remaining is negative and a

maximum impact factor is obtained in AWARE. A more comprehensive analysis of impact

assessment methods, including e.g. a correlation analysis of the WSI, Eco-scarcity, and other

methods along with an analysis of modelling choices has been accomplished by Boulay and

colleagues41.

Considering the methodological and numerical differences between WAVE+ and AWARE, it is

challenging to provide a clear recommendation on when to use which method. To a large extend

this depends on the goal and scope of the analysis and on the methodological preferences of the

user. If, for instance, the practitioner wants to include potential impacts on ecosystems, the

AWARE model should be preferred since the environmental water requirement of aquatic species

26

is considered in the available water remaining. If, however, the user wants to consider ground- and

surface water stocks in the scarcity assessment, the WAVE+ method should be used.

In general, WAVE+ tends to evaluate more countries as relatively water scarce compared to

AWARE (Figure S12) which can be considered a disadvantage if only few hotspots are to be

identified. However, this more conservative approach can also be advantageous if potential risks

shall not be underrepresented.

The consideration of atmospheric evaporation recycling by means of BIER in the WAVE+ method

is independent from the impact assessment step. Hence, BIER can be combined with other impact

assessment models, like AWARE, to assess the impacts of the effective water consumption

(Equation 1) only. This illustrates that the models are not competitive, provide individual strengths

and weaknesses and, thus, are recommended to be applied in parallel to analyze the water footprint

profile4 of the product systems under study.

In order to promote the applicability of the WAVE+ model, the BIER, BIERrunoff, WDI and

WAVE+ factors are made available free of charge in drainage basin, country and world region

resolutions on both monthly and annual levels in a Google Earth layer and a spreadsheet:

http://www.see.tu-berlin.de/wave/parameter/en/

Supporting information

Additional explanations, figures, and tables are available in the Supporting Information. These

documents are available free of charge via the internet at http://pubs.acs.org.

http://www.see.tu-berlin.de/wave/parameter/en/http://pubs.acs.org/

27

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